We have synthesized R5Pb3 (R = Gd-Tm) compounds in polycrystalline form and performed structural analysis, magnetization, and neutron scattering measurements. For all R5Pb3 reported here the Weiss temperatures {theta}W are several times smaller than the ordering temperatures TORD, while the latter are remarkably high (TORD up to 275 K for R = Gd) compared to other known R-M binaries (M = Si, Ge, Sn and Sb). The magnetic order changes from ferromagnetic in R = Gd, Tb to antiferromagnetic in R = Dy-Tm. Below TORD, the magnetization measurements together with neutron powder diffraction show complex magnetic behavior and reveal the existence of up to three additional phase transitions. We believe this to be a result of crystal electric field effects responsible for high magnetocrystalline anisotropy. The R5Pb3 magnetic unit cells for R = Tb-Tm can be described with incommensurate magnetic wave vectors with spin modulation either along the c axis in R = Tb, Er and Tm or within the ab-plane in R = Dy and Ho.